submitted to Mathematics (MDPI) for publication on 8/12/2021.
Yee Meng Teh 1, R.U. Gobithaasan 2 *, Kenjiro T. Miura 3, Diya’ J. Albayari 4, and Wen Eng Ong 1
- School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, Malaysia; veostly_0405@hotmail.com (Y.M.T.); weneng@usm.my (W.E.O.)
- Special Interest Group on Modelling & Data Analytics, Faculty of Ocean Engineering Technology and In-formatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia; gr@umt.edu.my
- Graduate School of Science & Technology, Shizuoka University, Hamamatsu, Shizuoka, 432-8561, Japan; miura.kenjiro@shizuoka.ac.jp
- Mathematics Department, Ibn Rushd National Academy-International section IB®, 17126 Amman, Jordan; diyabayari@gmail.com
- Correspondence: gr@umt.edu.my
In this work, we introduce a new type of surface called Log Aesthetic patch (LAP). This surface is an extension of Coons surface patch where the four boundary curves are either planar or spatial Log Aesthetic curves (LACs). To identify its versatility, we approximated Hyperboloid parabo-loid to LAP using the information of lines of curvature (LoC). The outer part of LoCs which role played as the boundary of Hyperboloid paraboloid are replaced with LACs before constructing the LAP. Since LoCs are essential in shipbuilding for hot and cold bending processes, we investi-gated LAP in terms of LoC’s curvature, its derivative of curvature, torsion, and Logarithmic Curvature Graph (LCG). Numerical results indicate that the LoCs for both the surfaces possess monotonic curvatures. An advantage of LAP approximation over its original Hyperboloid para-bolic is, the LoCs of LAP can be approximated to LACs, hence the first derivative of curvatures for LoCs are monotonic, whereas non-monotonic for hyperboloid parabolic. This confirms that the LAP produced is indeed of high-quality. Lastly, we project the LAP onto a plane using geodesic curvature to create strips which can be pasted together mimicking hot and cold bending processes in shipbuilding industry.
Keywords: log aesthetic curves; log aesthetic space curves; surface design; Coons patch; Lines of curvature.